Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in JAVA):

Solution:

import java.io.*;
import java.util.*;

public class Main {

    static int R;
    static int C;
    static int[][] board;

    static List<String> moves = new ArrayList<>();

    public static void main(String[] args) throws Exception {
        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));
        String[] parts = reader.readLine().split(" ");
        R = Integer.parseInt(parts[0]);
        C = Integer.parseInt(parts[1]);
        board = new int[R][C];

        for (int i = 0; i < R; i++) {
            parts = reader.readLine().split(" ");
            for (int j = 0; j < C; j++) {
                board[i][j] = Integer.parseInt(parts[j]);
            }
        }

        normalize();

        for (;;) {
            boolean hasNonZero = false;
            for (int i = 0; i < R; i++) {
                for (int j = 0; j < C; j++) {
                    if (board[i][j] == 0) {
                        if (!releaseRow(i)) {
                            System.out.println(-1);
                            return;
                        }
                        if (!releaseColumn(j)) {
                            System.out.println(-1);
                            return;
                        }
                    }
                    else {
                        hasNonZero = true;
                    }
                }
            }

            if (!hasNonZero) {
                break;
            }
        }

        System.out.println(moves.size());
        for (int i = 0; i < moves.size(); i++) {
            System.out.println(moves.get(i));
        }
    }

    private static boolean releaseColumn(int c) {
        for (int i = 0; i < R; i++) {
            if (board[i][c] > 0) {
                if (!drop("row " + (i + 1), i,i + 1, 0, C, board[i][c])) {
                    return false;
                }
            }
        }
        return true;
    }

    private static boolean drop(String message, int fromR, int toR, int fromC, int toC, int times) {
        for (int i = fromR; i < toR; i++) {
            for (int j = fromC; j < toC; j++) {
                board[i][j] -= times;

                if (board[i][j] < 0) {
                    return false;
                }
            }
        }

        for (int k = 0; k < times; k++) {
            moves.add(message);
        }

        return true;
    }

    private static boolean releaseRow(int r) {
        for (int i = 0; i < C; i++) {
            if (board[r][i] > 0) {
                if (!drop("col " + (i + 1), 0,R, i, i + 1, board[r][i])) {
                    return false;
                }
            }
        }
        return true;
    }


    private static void normalize() {
        int min = Integer.MAX_VALUE;
        for (int i = 0; i < R; i++) {
            for (int j = 0; j < C; j++) {
                min = Math.min(board[i][j], min);
            }
        }

        if (min > 0) {
            for (int i = 0; i < min; i++) {
                int till = C;
                String prefix = "col ";;
                if (R < C) {
                    till = R;
                    prefix = "row ";
                }

                for (int j = 0; j < till; j++) {
                    moves.add(prefix + (j + 1));
                }
            }
        }

        for (int i = 0; i < R; i++) {
            for (int j = 0; j < C; j++) {
                board[i][j] -= min;
            }
        }
    }


}